Josh S Thompson said:is there a proof?
Covariance is a measure of the direction and strength of the relationship between two variables. It indicates how much two variables change together. The correlation coefficient, on the other hand, is a standardized measure of the same relationship, which takes into account the scales of the variables and ranges from -1 to +1.
A positive covariance or correlation coefficient indicates a positive relationship between the two variables. This means that as one variable increases, the other variable also tends to increase. The strength of the relationship depends on the magnitude of the covariance or correlation coefficient.
A negative covariance or correlation coefficient indicates a negative relationship between the two variables. This means that as one variable increases, the other variable tends to decrease. Again, the strength of the relationship is determined by the magnitude of the covariance or correlation coefficient.
To calculate covariance, you need to first calculate the mean of both variables. Then, for each data point, subtract the mean of each variable from its value and multiply them together. Finally, add up all of these values and divide by the total number of data points. To calculate correlation coefficient, you need to first calculate the covariance. Then, divide the covariance by the product of the standard deviations of the two variables.
No, neither covariance nor correlation coefficient can be used to determine causation. They only measure the relationship between two variables, but do not indicate which variable is causing the other. Causation can only be determined through further experimentation and analysis.